SUMMARY 1 BAD 376 PROBLEM ANALYSIS: REGRESSION ANALYSIS Consider the following simple linear regression: Y-B+BX, Objective: the objective is to use a sample to estimate B. and ẞ, .To do that, we use Ordinary Least Squares Method (OLS). This is how to estimate ẞ, and ẞ, using Ordinary Least Squares Method: Step 1: compute the mean of X and the mean of Y; that is X and Y Step 2: compute the variance of X; that is, VAR(X) Step 3: compute the covariance between X and Y; that is, COV(X, Y) Step 4: compute B, using this formula: COV( X,Y) VAR( X ) Step 5: compute B, using this formula: B₁ =Y-B₁xX The coefficient of Determination (R²) QUESTION 1: R² B₁XCOV( X,Y) VAR( Y ) The following table contains data on X and Y: X₁ Y₁ 3 6 5 4 7 2 Consider the following regression line: Y =ẞ₁ +B,X. 1. Use Ordinary Least Squares Method to estimate B. and B,; 2. Find the prediction line; 3. Compute R². SUMMARY 2 Consider the following simple regression: Ý, B, +‚ׂ. = To conduct the statistical test that the slope is equal to zero, that is, B₁ = 0, involves the following steps: Step1: The null Hypothesis Ho: B₁ = 0 Step 2: The alternative Hypothesis HA: B₁ #0 Step 3: T-statistic: =- B₁-0 SE Where, is the estimate of B SE: the standard error Step 4: Decision criteria. To decide whether to reject Ho or not you need to compare the absolute value of t (t) with taz Where: 1. If > 2. If t